The tandem differential mobility analyzer (TDMA) is useful for studying phenomena that lead to size changes in submicron aerosol particles. Evaporation, condensation and chemical reactions within airborne droplets are examples of such phenomena. With this method, aerosols of a known size are selected with a differential mobility analyzer (DMA). These monodisperse aerosols then undergo processes that result in growth or shrinkage; the extent of growth or shrinkage is determined with a second DMA. In this paper, a theoretical treatment of a TDMA system is presented, and procedures for laboratory implementation are discussed. The theory is presented in an analytic form that can be encoded for on-line or off-line data analysis. Statistical techniques are used to calculate the precision with which size changes can be determined, and results of these analyses are confirmed experimentally. It is shown that diameter changes can be measured with a precision of about 0.3% using available instrumentation. For aerosols in the 0.01-0.2 μm diameter range where the technique works best, this corresponds to diameter changes of 0.03-0.6 nm, or the characteristic thickness of a monolayer.